Question: Solve for $x$ and $y$ using elimination. ${6x-6y = -6}$ ${5x+5y = 15}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $6$ ${30x-30y = -30}$ $30x+30y = 90$ Add the top and bottom equations together. $60x = 60$ $\dfrac{60x}{{60}} = \dfrac{60}{{60}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {6x-6y = -6}\thinspace$ to find $y$ ${6}{(1)}{ - 6y = -6}$ $6-6y = -6$ $6{-6} - 6y = -6{-6}$ $-6y = -12$ $\dfrac{-6y}{{-6}} = \dfrac{-12}{{-6}}$ ${y = 2}$ You can also plug ${x = 1}$ into $\thinspace {5x+5y = 15}\thinspace$ and get the same answer for $y$ : ${5}{(1)}{ + 5y = 15}$ ${y = 2}$